OC-IV
This presentation is the property of its rightful owner.
Sponsored Links
1 / 13

OC-IV PowerPoint PPT Presentation


  • 65 Views
  • Uploaded on
  • Presentation posted in: General

OC-IV. Orbital Concepts and Their Applications in Organic Chemistry. Klaus Müller. Script ETH Zürich, Spring Semester 2010. Chapter 3. s-Character balancing for central atom hAO’s Ligand geometries around central atoms.

Download Presentation

OC-IV

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Oc iv

OC-IV

Orbital Concepts

and

Their Applications in Organic Chemistry

Klaus Müller

Script

ETH Zürich, Spring Semester 2010

Chapter 3

s-Character balancing for central atom hAO’s

Ligand geometries around central atoms


Oc iv

In principle, sp3 hAO‘s is a good starting point for a tetrahedrally coordinated

central atom, even if the ligand geometry deviates somewhat from an ideal

tetrahedral geometry.

There may be various reasons for he observation of ligand geometries that

deviate markedly from ideal tetrahedral coordination:

- steric interactions between the ligands

- electronic interactions between the ligands other than steric

- non-tetrahedral valence angle(s) when ligands are involved in rings

- different electronegativities of the ligands

electropositive ligand

the s-LMO is polarized

towards the central atom;

the coefficient cs at the

central atom for this s-LMO

is comparatively large;

electronic energy lowering

by shifting s-character from

low-amplitude hAO domain to

high-amplitude hAO domain

hence, any change in

s-character of the hAO

of the central atom will be

strongly felt by this s-LMO

electronegative ligand

the s-LMO is polarized

towards the ligand;

the coefficient cs at the

central atom for this s-LMO

is comparatively small;

Bent‘s rule:

a central atom increases the

s-character of its hAOs oriented

towards electropositive ligands

at the expense of s-character

in hAO‘s towards electronegative

ligands, i.e.,

hence, any change in

s-character of the hAO

of the central atom will be

little felt by this s-LMO

a central atom does not waste s-character

towards electronegative ligands


Oc iv

112.1°

114.7°

115.9°

106.7°

103.8°

102.4°

hypothetical ligand

of zero electronegativity

s-LMO polarized towards central atom;

any gain in s-character of center hAO

results in marked energy gain of s-LMO

s-LMO in the extreme

becomes a lonepair orbital

s-LMO polarized towards electronegative

ligand atom; any change in s-character of

center hAO has little effect on energy of s-LMO

valence electron sextett

108.4°

120.0°

110.5°

hypothetical ligand

of infinite electronegativity

s-LMO polarized towards electronegative

ligand atom; any change in s-character of

center hAO has little effect on energy of s-LMO

s-LMO in the extreme

becomes an empty hAO;

no s-character is wasted

for empty orbital: hence,

empty orbital is pure p-AO;

→ planar geometry

s-LMO polarized towards central atom;

any gain in s-character of center hAO

results in marked energy gain of s-LMO

three s-LMO‘s receive all s-character

in symmetrical case: three sp2-hAO‘s;

geometry is trigonal planar


Oc iv

y

g

f2

x

f1

g

180°

170°

160°

1

150°

1 -

2

140°

cp

130°

120°

2

- cs

110°

2

1 - cs

100°

90°

hAO p-character

50%

60%

70%

80%

80%

100%

hAO s-character

50%

40%

30%

20%

10%

0%

sp

sp2

sp3

sp5

p

relationships between

s- and p-character of two equivalent hAO‘s

and the interorbital axis angle g

2

2

f1 = cs.s + cp.px

normalization : cs + cp = 1

2

2

f2 = cs.s + cp. (cosg.px + sing.py)

orthogonality : cs + cp.cosg = 0

2

2

hence : 1 - cp + cp.cosg = 0

1

2

p-character : cp=

1 - cosg

-cosg

2

s-character : cs=

1 - cosg

g from p-character : cosg=

g from s-character : cosg=


Oc iv

alkyl

108.4° ± 2.6°

109.6° ± 1.8°

111.3° ± 2.0°

112.7° ± 0.2°

108.1° ± 2.2°

109.1° ± 2.0°

111.0° ± 1.5°

110.9° ± 0.2°

104.5°

92.1°

90.6°

90.3°

111.7°

98.9°

96.2°

106.6

92.2

87.8

1.714

1.855

1.362

..

..

0.14 - 0.20 Å

q = 67°

q

q = 3.5° ± 3.7°

q ~ 70°!

X-ray of

1-benzyl-

phosphole

(BZPHOS10)

pyrroles essentially planar

p-conjugation pays for

lone pair spx→ p promotion


Oc iv

+

+

106.7°

109.8°

119.7°

110.9°

107.1°

102.4°

93.3°

98.9°

101.7°

113.0°

q

q

q

q

q = 59.1° ± 3.4°

q = 49.3° ± 3.5°

q = 46.3° ± 6.5°

q = 49.1° ± 5.7°

0.66 ± 0.04 Å

0.51 ± 0.04 Å

0.43 ± 0.06 Å

0.44 ± 0.05 Å

h (pyr.height)

~ 19 kcal/mol

~ 10 kcal/mol

~ 8 kcal/mol

~ 8 kcal/mol

N

inversion barrier

e-

hn

IP1

9.9 eV

9.0 eV

8.8 eV

8.7 eV

8.0

11.3

11.3

11.1

pKa(R=H)

7.9

-

10.3

10.1

pKa(R=CH3)

amine basicity (in H2O)

215.7 kcal/mol

222.7

224.3

225.4 kcal/mol

PA (R=H)

221.5 kcal/mol

-

227.8

228.8 kcal/mol

PA (R=CH3)

proton affinity in gas-phase


Oc iv

DGN-inv

~ 8 kcal/mol

13-16 kcal/mol

26-30 kcal/mol

very slow at RT

very fast at RT

fast at RT

rates (RT)

~ 107 sec

~ 103 – 101 sec

~ 10-6 – 10-9 sec

t1/2 (RT)

~ 10-7 sec

~ 10-3 – 10-1 sec

~ 106 – 109 sec

~ 10d– 10y

first diastereomeric cis- and trans-

N-methoxy isoxazolidin derivatives

isolated by

K. Müller & A.Eschenmoser,

Helv.Chim.Acta 52, 1823 (1969)

DGN-inv

~ 18-20 kcal/mol

25-28 kcal/mol

>32 kcal/mol

very slow at RT

fast at RT

very slow at RT

first diastereomeric cis- and trans-

N-Cl-aziridine derivatives isolated by

A.Eschenmoser & D. Felix,

Angew. Chem IE 7, 224 (1968)

DGN-inv

~ 28-32 kcal/mol

~ 26-28 kcal/mol

very slow at RT

very slow at RT


Oc iv

kB.T

DG#

.

e

k =

RT

h

t1/2 = ln2 / k

T

k (sec-1)

-80°C

0°C

25°C

100°C

DG#

5

9.106

6.108

1.109

9.109

kcal/mol

10

2.101

6.104

3.105

1.107

5.10-5

7.101

6.100

1.104

15

1.10-10

20

6.10-4

2.10-2

2.101

7.10-8

25

3.10-16

3.10-6

2.10-2

6.10-22

7.10-12

30

8.10-10

2.10-5

t1/2 (sec)

T

-80°C

0°C

25°C

100°C

DG#

5

7.10-8

1.10-9

5.10-10

7.10-11

kcal/mol

10

1.10-5

2.10-6

6.10-8

3.10-2

15

~4h

1.10-1

1.10-2

5.10-5

20

5.101

4.10-2

~200y

~20min

~108y

3.101

25

~120d

~2d

~8h

30

~1013y

~3000y

~30y


Oc iv

z

z

z

y

y

y

x

x

x

hAO2 = csss + csp (cosj (- py + px) – sinj pz)

hAO3 = csss + csp (cosj (- py - px) – sinj pz)

2

2

cns + 3 css = 1 (1 valence s-AO available, eq 2)

2

2

2

cnpz + 3 csp sin j = 1 (1 valence pz-AO, eq 3)

2

2

1

3

3

3

2

2

3 csp cos j = 2 (2 valence px,y-AO‘s, eq 4)

2

2

cns + cnpz = 1 (n-HAO normalized, eq 1)

1

1

√3

√3

2

2

2

2

2

2

csp =

csp =

2

2

2

cnpz =

css =

cns =

quantitative relationships between hAO s- and p-characters

for a trigonal pyramidal center with a lone pair as a function of ligand geometry

r

r

j

j

r

g

r

d

1 lonepair spn hybrid-AO

pojnting along z-axis

3 equivalent spm hybrid-AO‘s

pojnting along axes

of trigonal pyramid

relationship between

out-of-plane angle j

and valence bond angle g

d2 = 2r2 – 2r2 cos g

d2 = 2r2 – 2r2 cos 120°

r= r cosj

cos2j = (1 – cosg)

hAOn = cnss + cnpzpz

hAO1 = csss + csp (cosj py – sinj pz)

contraints and normalization:

1

1

(from eq 4)

hence:

cos j

1 - cosg

2

- 3 cosg

2

2

cnpz = 1 – 2 tg j

(from eq 3)

1 - cosg

1 + 2 cosg

2

2

cns = 2 tg j

(from eq 1)

1 - cosg

- cosg

2

2

css = (1 - 2 tg j)

(from eq 2)

1 - cosg


Oc iv

120

110

3

2

cosg = 1 - cos j

2

100

90

2

2

80

cos j

cos j

70

- 2

3

cosq =

60

4 - 3

50

40

30

20

10

0

q

j

g

35

30

25

20

15

10

5

0

5

10

15

20

25

30

35

j

e(p)

e(s-hAO)

e(sp3)

e(sp2)

e(n-hAO)

e(s)

for extreme pyramidalities,

the poor s-orbital overlap of

a p-AO with the ligand hAO,

results in a destabilization of

the s-LMOs

e(s-LMO)

in this domain, the s-LMO‘s show

a rather flat energy response to the

rehybridization of the hAO‘s at the

central atom; this response is the

weaker the more the s-LMO‘s are

polarized towards electronegative

ligands; hence, in this domain, the

energy of the doubly occupied lone

pair orbital dictates the geometry

by pulling as much s-character as

possible from the hAO‘s involved

in the s-LMO‘s

trig

tet

tet

q = tet/2


Oc iv

quantitative relationships between hAO s- and p-characters

for a tetrahedral center with two different sets of ligands

z

z

z

y

y

y

x

x

x

2

2 sin gA/2 = 1 – cos gA

2

2

2 csA + 2 csB = 1

2

2

2

2

2 cpB sin gB/2 = 1

2 cpA sin gA/2 = 1

2

2

2

2

csB + cpB = 1

csA + cpA = 1

1

1

2

cpA = =

2

2 sin gA/2

1 - cos gA

- cos gA

1

2

csA = 1 - =

1 - cos gA

1 - cos gA

2

1 – 2 csA

1 + cos gA

2

csB = =

2

2 (1 - cos gA)

_

_

_

1 + cos gA

cos gB = = –

+

+

+

1 - 3 cos gA

2

2

1 – 3 cos gA

cpB = 1 – csB =

2 (1 - cos gA)

2

2

cpB - 1

cpB - 1

2

2

≈ cos gAd

cpB

cpB

+

2

2

√2

√2

3

3

√2

2 equivalent

spm hAO‘s

along Z-A axes

A

A

A

A

A

A

gA

B

B

B

gB

2 equivalent

spn hAO‘s

along Z-B axes

B

B

B

hAOA1,2 = csA s + cpA (cos gA/2 pz± sin gA/2 py)

gA given; gB = f(gA)

hAOB3,4 = csB s + cpA (- cos gB/2 pz± sin gB/2 px)

contraints and normalization:

(1 s-valence AO, eq 1)

(1 py-valence AO, eq 2)

(1 px-valence AO, eq 3)

(normalization, eq 4)

(normalization, eq 5)

(from eq 2)

hence:

(from eq 4)

(from eq 1)

(from eq 5)

(from eq 3)

angular deviation: gA = (tet) ± d

cos (gA ± d) = cos gA cos d sin gA sin d

1+ cos gAd

1 + cos gA

1

d

cos gB = = – ≈ =

(1 )

hence:

3

1 – 3 cos gA

2

opening of gA results in closing of gB and vice versa; and

hence:

increase in s-character in hAOA‘s and decrease in s-character in HAOB‘s


Oc iv

1 + cos gA

1 + cos gA

cos gB = –

cos gB = –

1 – 3 cos gA

1 – 3 cos gA

Search in Cambridge Structural DatabaseA = {Ctet}

B = {N, O, F, P, S, Cl}

all bonds acyclic at central C

results in 253 X-ray structures:

gB

108.3°

gA

113.7°

gB

1 + cos gA

cos gB = –

1 – 3 cos gA

gB = tet

gB = 107.5° ± 3.2°

gA-gB scattergram

gA

gA = tet

gA = 115.4° ± 3.0°

Search in Cambridge Structural DatabaseA = {C, N, O, F)

all bonds acyclic at central C

results in 12‘624 X-ray structures:

gB

gB

gA

1 + cos gA

cos gB = –

1 – 3 cos gA

gB = tet

gA-gB scattergram

gA

gA = tet


Oc iv

114.7° ± 4.6°

109.9° ± 4.1°

108.5° ± 4.0°

108.0° ± 3.4°

113.2° ± 1.5°

110.4° ± 1.2°

108.1° ± 2.0°

107.6° ± 1.1°

115.9° ± 2.0°

110.6° ± 1.3°

110.9° ± 3.5°

109.7° ± 1.9°

no equivalent orthonormal spx hAOs

possible for bond vectors of < 90°

interbond angle

equivalent orthonormal spx hAOs

along bond vectors of 90° interbond

angle would be pure p-AOs resulting

in poor s-LMOs and unacceptable

angle (180°!) for exocyclic (sp) hAOs

two equivalent spx hAOs (ca. sp5)

defined by equivalent hAOs (ca. sp2)

along exocyclic bond axes;

two equivalent spx hAOs (ca. sp3)

defined by equivalent hAOs along

exocyclic bond axes

sp5 hAO axes deviate ca.20° from

CC bond axes of cyclopropane;

off-axis hAOs result in significantly

bent s-LMOs (s*-LMOs)

sp3 hAO axes deviate only ca.10°

from CC bond axes of cyclobutane; off-axis hAOs result in only slightly

bent s-LMOs (s*-LMOs)


  • Login